Finite Group Databasebeta

← #18009458

Subgroups — #18009458

Order 4736.

228 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 228 conjugacy classes of subgroups — too many to draw. Only its 54 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D37⋊(C22⋊C8)C211yesmaximal, characteristic
2#14558475C211yesmaximal, characteristic
3#14557392C211yesmaximal, characteristic
4C2×D37⋊C8C412yescomplemented
5C2×C4⋊#3866—21no—
6C2×C22⋊#3866—21no—
7#11924593—21no—
8C22⋊#64438—21no—
9(C2×#3866)⋊C4C412yescomplemented
10C22×C4×D37C2211yescharacteristic
11C2×#10596936—21no—
12C2×#10596938—21no—
13#11924443C411yescharacteristic, complemented
14#95×C37C411yescharacteristic, complemented
15C23×D37D411yescharacteristic
16C22×#3866—22no—
17C22×C4×C37—21no—
18C22×C4×C37C2×C411yescharacteristic
19C22×Dic37—21no—
20C22×Dic37D411yescharacteristic
21C2×C4×D37—42no—
22C2×C4×D37C2×C411yescharacteristic
23C2×C4×D37C2×C411yescharacteristic
24C2×C4×D37D411yescharacteristic
25C2×C4×D37Q811yescharacteristic
26C22⋊#3866—41no—
27C22⋊#3866—41no—
28C2×#64438—22no—
29C4⋊#3866—42no—
30D37⋊C8—42no—
31#10596938—41no—
32#10596938—41no—
33#10596936—42no—
34C23×C37C22⋊C411yescharacteristic
35C22×D37—41no—
36C22×D37—41no—
37C22×D37C22⋊C411yescharacteristic
38C22×D37C4⋊C411yescharacteristic
39C22×D37D811yescharacteristic
40C22×D37SD1611yescharacteristic
41C22×D37SD1611yescharacteristic
42C22×D37Q1611yescharacteristic
43C2×#3866—42no—
44C2×#3866—42no—
45C2×#3866—42no—
46C2×C4×C37—41no—
47C2×C4×C37—41no—
48C2×C4×C37—41no—
49C2×C4×C37—41no—
50C2×C4×C37C4211yescharacteristic
51C2×C4×C37C4⋊C411yescharacteristic
52C2×Dic37—22no—
53C2×Dic37—41no—
54C2×Dic37—41no—
55C2×Dic37—41no—
56C2×Dic37C22⋊C411yescharacteristic
57C2×Dic37C4⋊C411yescharacteristic
58C4×D37—22no—
59C4×D37—22no—
60C4×D37—41no—
61C4×D37—41no—
62#64438—42no—
63C22×C37—21no—
64C22×C37—21no—
65C22×C37#9511yescharacteristic
66C22×C37#10211yescharacteristic
67C22×C37#10311yescharacteristic
68C2×D37—21no—
69C2×D37—21no—
70C2×D37—21no—
71C2×D37—21no—
72C2×D37—41no—
73C2×D37—41no—
74C2×D37—41no—
75C2×D37—41no—
76C2×D37#10211yescharacteristic
77C2×D37#10311yescharacteristic
78C2×D37#10611yescharacteristic
79C2×D37#10711yescharacteristic
80#3866—82no—
81C4×C37—21no—
82C4×C37—21no—
83C4×C37—81no—
84Dic37—21no—
85Dic37—81no—
86Dic37#9912yes—
87#1289—371nomaximal, Sylow
88C2×C37—21no—
89C2×C37—21no—
90C2×C37H(3,ℤ/4)11yescharacteristic
91C2×C37#34011yescharacteristic
92C2×C37#34211yescharacteristic
93D37—21no—
94D37—21no—
95D37—21no—
96D37—21no—
97C2×C22⋊C8—371no—
98#380—371no—
99#380—371no—
100C37#128911yescharacteristic, complemented, Sylow
101C23×C4—371no—
102C22×C8—372no—
103C2×C4⋊C4—741no—
104C2×C4⋊C4—741no—
105C2×C22⋊C4—741no—
106C2×C22⋊C4—741no—
107C22⋊C8—741no—
108C22⋊C8—741no—
109#95—372no—
110#95—371no—
111#95#386611yescharacteristic, complemented
112C24—371no—
113C22×C4—21no—
114C22×C4—371no—
115C22×C4—371no—
116C22×C4—371no—
117C22×C4—371no—
118C22×C4—371no—
119C22×C4—742no—
120C22×C4—741no—
121C22×C4—1482no—
122C22×C4C2×#386611yescharacteristic
123C2×C8—742no—
124C2×C8—1482no—
125C4⋊C4—1482no—
126C4⋊C4—1482no—
127C22⋊C4—1481no—
128C22⋊C4—1481no—
129C22⋊C4—1481no—
130C22⋊C4—1481no—
131C23—371no—
132C23—371no—
133C23—371no—
134C23—371no—
135C23—371no—
136C23—371no—
137C23—1481no—
138C23—1481no—
139C23C22⋊#386611yescharacteristic
140C2×C4—41no—
141C2×C4—41no—
142C2×C4—41no—
143C2×C4—41no—
144C2×C4—371no—
145C2×C4—371no—
146C2×C4—742no—
147C2×C4—742no—
148C2×C4—742no—
149C2×C4—1481no—
150C2×C4—1481no—
151C2×C4—1481no—
152C2×C4—1481no—
153C2×C4—1482no—
154C2×C4—1482no—
155C2×C4—1482no—
156C2×C4—1481no—
157C2×C4C4×#386611yescharacteristic
158C2×C4C4⋊#386611yescharacteristic
159C8—1482no—
160C22—21no—
161C22—21no—
162C22—371no—
163C22—371no—
164C22—371no—
165C22—371no—
166C22—741no—
167C22—741no—
168C22—741no—
169C22—741no—
170C22—1481no—
171C22—1481no—
172C22—1481no—
173C22—1481no—
174C22(C2×#3866)⋊C411yescharacteristic
175C22#1192459811yescharacteristic
176C22#1192459911yescharacteristic
177C4—21no—
178C4—21no—
179C4—81no—
180C4—372no—
181C4—2961no—
182C4—2962no—
183C4—741no—
184C2—21no—
185C2—21no—
186C2—741no—
187C2—741no—
188C2—741no—
189C2—741no—
190C2#1455840011yescharacteristic
191C2#1455840611yescharacteristic
192C2#1455841011yescharacteristic
subgroupG/H
centerC22(C2×#3866)⋊C4
commutatorC2×C4×C37C42
FrattiniC22×C4C2×#3866
Fitting#95×C37C4
socleC22×C37#95
prime radicalC23×D37D4
cosocleC22×C4×D37C22
hypercenter#95#3866
hypocenterC37#1289
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ #95

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
4. C2×D37⋊C8C4semidirect
9. (C2×#3866)⋊C4C4semidirect
13. #11924443C4semidirect
14. #95×C37C4semidirect
100. C37#1289semidirect
111. #95#3866semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
D37⋊(C22⋊C8)2
#145584752
#145573922
#128937